Course

Unit I

Review of probability concepts – conditional probability- Bayes theorem. Random Variable and Distributions: Introduction to random variables – discrete and continuous random variables and their distribution functions- mathematical expectations – moment generating function and characteristic function.

Unit II

Binomial, Poisson, Geometric, Uniform, Exponential, Normal distribution functions (moment generating function, mean, variance and simple problems) – Chebyshev’s theorem.

Unit III

Stochastic Processes: General concepts and definitions – stationary in random processes – strict sense and wide sense stationary processes – autocorrelation and properties- special processes – Poisson points, Poisson and Gaussian processes and properties- systems with stochastic inputs – power spectrum- spectrum estimation, ergodicity –Markov process and Markov chain, transition probabilities, Chapman Kolmogrov theorem, limiting distributions classification of states. Markov decision process.

Lab Practice Problems

Implementation of various statistical measures like, mean, mode and deviations. Linear regression and correlations. Implementation of statistical distributions and Markovian models.

Course objectives

• To understand the concepts of basic probability and random variables.
• To understand some standard distributions and apply them to some problems.
• To understand the concepts of random process, stationarity, and autocorrelation functions.
• To understand Markov process and Markov chain and related concepts.

Course Outcomes

CO1: Understand the basic concepts of probability and probability modeling.

CO2: Understand statistical distributions of one- and two-dimensional random variables and correlations.

CO3: Understand the basic concepts of stochastic processes and stationarity.

CO4: Understand the purpose of some special processes.

CO5: Understand spectrum estimation and spectral density function.

CO-PO Mapping

Evaluation Pattern: 70:30

Textbook(s)

Douglas C. Montgomery and George C. Runger, “Applied Statistics and Probability for Engineers”, (2005) John Wiley and Sons Inc.

Papoulis, and Unnikrishna Pillai, “Probability, Random Variables and Stochastic Processes”, Fourth Edition, McGraw Hill, 2002.

Reference(s)

Ravichandran, “Probability and Random Processes for Engineers”, First Edition, IK International, 2015.

Scott L. Miller, Donald G. Childers, “Probability and Random Processes”, Academic press, 2012.

Lab Experiments:

1. Finding statistical measures like mean, variance, standard deviation, mode and moments for given data
2. Use of ‘pdf’,’cdf’,’icdf’ commands for finding probabilities if random variable follows Binomial, Poisson, uniform exponential and normal distributions
3. Generation of sample data from populations with various discrete distributions
4. Generation of sample data from populations with various continuous distributions
5. Multilinear Regression
6. Evaluation of Covariance and Correlation using excel/MATLAB
7. Multinomial and multinormal distributions
8. Generation of Multivariate Data